24. Design theory of Chebyshev low-pass filter based on prototype (insertion loss method)
Prototype-based filter design is a basic method of design. Although there are more powerful automated tools that can replace it, it still needs to be understood if theoretical research is to be carried out.
The original intention of writing this article is not to introduce the Chebyshev low-pass filter design theory, but to find that some domestic articles confuse the low-pass filter network with the low-pass filter matching network . Design a low-pass filter matching network using the design prototype of a low-pass filter network.
The low-pass filter matching network actually adds an impedance transformation function on the basis of filtering. Its design parameters include impedance transformation ratio, design bandwidth parameters, etc. Because of its good matching characteristics, it is often used in the design of power amplifiers. middle. Such as the MTT article:
Design of Highly Efficient Broadband Class-E Power Amplifier Using Synthesized Low-Pass Matching Networks
The following first introduces the prototype-based Chebyshev low-pass filter design theory (insertion loss method), and introduces the use of equivalent principles to convert it into a microstrip line circuit.
1 Introduction to Insertion Loss Method
The insertion loss method seems to be very high-level, but it is actually a simple look-up process for the designer. You can refer to the article:
Insertion loss method design low-pass prototype filter (2): Equal ripple low-pass filter design
here To illustrate again, the design parameters are as follows:
1. Cut-off frequency: 3.8GHz
2. In-band ripple: 0.5dB
3. The attenuation reaches more than 60dB at 7.6GHz
2 Insertion loss method Look up the table according to the design requirements
The first step in the design of the insertion loss method is to look up the table according to the requirements of the in-band ripple. Here, the requirement for the in-band ripple is less than 0.5dB. Find the following chart (the component value table of the Chebyshev low-pass filter ) :
The design requirement is to attenuate above 60dB when 2f0=7.6, and the value of the abscissa at this time is (7.6/3.8-1)=1, that is, the attenuation must be above 60dB when the abscissa is 1. N should choose an odd number, choose N=7 at this time.
Next, we need to look up the value of N and the value of insertion loss. The table is as follows:
mainly look at the value when N=7. You can see that when N=7, 8 components are needed, that is, 4 An inductor and capacitor:
here you can get the prototype of the design.
3 Prototype-based design of lumped parameter filters
For the conversion principle of the design, please refer to:
Hong J S. Microstrip filters for RF/microwave applications[J]. IEEE Microwave Magazine,
2002, 3(3):62-65
Put the formula directly here:
the above wc is the angular frequency, wc=2 pi f, Z0 is the port impedance, generally set to 50 ohms, gc and gl are the components obtained from the table lookup, for example, the components obtained from the table lookup above The first part of the device is 1.7372. If you want the first one to be an inductance, use the first formula to calculate the inductive reactance. If you want the first one to be a capacitor, use the first formula to calculate the capacitive reactance. This is your choice. of. But if the first is an inductor, the second must be a capacitor, the third must also be an inductor, and so on.
In order to facilitate everyone's calculation, I wrote a Matlab code:
clear all
clc
f=3.8e9;%设置截止频率
Z0=50;%设置端口阻抗
g=1.7372;
L=Z0*g/(2*pi*f);
C=g/(Z0*2*pi*f);
disp(['如果是电感，电感值为：',num2str(L*1e9),'nH'])
disp(['如果是电容，电容值为：',num2str(C*1e12),'pF'])
When designing here, I adopted the first mode of inductance. The parameter g of the first one is 1.7372. I assigned and calculated the following results:
because it is an inductance, the inductance value obtained here is 3.6379nH, so the first one at the beginning An inductance value is 3.6379nH. Substituting different g in turn to calculate the values of other concentrated parameters, the following circuit diagram is obtained:
Run the simulation to get the S parameter results, it can be seen that the ripple in the passband does not meet the requirements, but the stopband attenuation reaches 70dB, here is just a demonstration. Fine-tuned:
4 Prototype-based design of distributed parameter filters
A filter with distributed parameters can be designed based on the prototype, and the more common one is the microstrip line filter. A very important equivalent is needed in the design. Here, refer to the description of other papers. Simply put, it is equivalent to using high and low impedance lines. The high impedance microstrip line is equivalent to an inductance, and the low impedance microstrip line is equivalent to Capacitance:
For the convenience of calculation, the Matlab code is directly written here:
clear all
clc
f=3.8e9;%设置截止频率
Z0=50;%设置端口阻抗
Zoh=90;%高阻抗线阻抗
Zol=20;%低阻抗线阻抗
epsilon=4.6;%设置板材介电常数
g=1.7372;
L=Z0*g/(2*pi*f);
C=g/(Z0*2*pi*f);
c=299792458;%光速
loh=L*c/(Zoh*sqrt(epsilon));
lol=C*Zol*c/sqrt(epsilon);
disp(['如果是电感，电感值为：',num2str(L*1e9),'nH，等效微带线长度为：',num2str(loh*1e3),'mm'])
disp(['如果是电容，电容值为：',num2str(C*1e12),'pF，等效微带线长度为：',num2str(lol*1e3),'mm'])
When designing here, I used the first mode of inductance. The first parameter g is 1.7372. After assigning and calculating the following results, it also means that the length of the first line is 5.6501mm: the line of other parameters can be calculated in
turn long. Secondly, the line width needs to be obtained. The FR4 plate is used here with a dielectric constant of 4.6, and the ADS calculation tool LineCalc is used for calculation: thus the line width of the
20-ohm low-impedance line under the plate is 10.8mm, and the height of the 90-ohm line is The line width of the impedance line is about 0.85mm, and the circuit diagram constructed from this is as follows:
Run the simulation and get the result:
you can see that the design requirements are basically met, but adjustments are still needed. I mainly focus on teaching here, so I won’t make fine-tuning .
ADS also has a convenient design tool based on this method, refer to the previous blog post:
10. ADS use record to design high and low impedance filters (including layout simulation)